Combined method for calculating raman band intensities with consideration for the dependence of the raman tensor on the frequency of exciting radiation

It is shown that at certain assumptions the tensor of Raman bands can be represented as a sum of the Placzek term and the fast convergent series that contains information on the sensitivity of the tensor elements to the frequency of exciting radiation. The convergences of the corresponding series and the frequency dependences of the Raman band intensities for particular molecules are studied by computer experiments. Vernadskii Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences. Moscow State Civil-Engineering University. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 2, pp. 241–249, March–April, 1996. Translated by I. Izvekova     

Effect of the components of the raman scattering tensor on band intensities

The Raman scattering (RS) tensor as a function of excitation radiation frequency is studied taking into account, the vibration quantum. It is shown that the corresponding asymmetric components of the tensor are described by fast converging series. Expressions are obtained for the antisymmetric and symmetric components of the RS tensor. A convenient formula is proposed for the calculation of the RS tensor and its components, where the tensor is represented as a sum of the derivative of static polarizability and the terms containing fast converging series. The formula makes it possible to avoid infinite summation. Computer experiments simulating the dependence of the intensity of RS bands and their components on the excitation frequency are carried out. Moscow State University of Building Engineering. V. I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 37, No. 6, pp. 1006–1015, November–December, 1996. Translated by I. Izvekova     

Estimation of the contributions of absorption bands for overtones and composite frequencies in infrared spectra of brominated and oxygen-containing organic compounds

Intensities of fundamental, overtone, and composite absorption bands for 27 brominated hydrocarbons and 20 oxygen-containing organic compounds are calculated in an anharmonic approach. The first and second derivatives of the electric dipole moment of the molecule with respect to normal coordinates are determined using ab initio quantum-chemical MP2/6-31G(1d) calculations. For the studied compounds, the average contributions of overtones and composite frequencies to absorption in the region 100–4000 cm⁻¹ is 4.8% for brominated hydrocarbons and 3.2% for oxygen-containing compounds. The major part of the contribution of overtones and composite frequencies falls into the regions (mainly from 1600 to 2800 cm⁻¹) where fundamental transitions are observed rarely. The calculation performed well describe the positions of maxima and the intensities of fundamental, overtone, and composite absorption bands and can be used for the standardless spectrochemical analysis of compounds by their overtone spectra.     

Vibrational structure of the electronic transition to the third excited singlet state of pyridine N-oxide

The electronic absorption spectrum of pyridine N-oxide vapor in the region of the third electronic transition (43,000-46,000 cm_-1) was recorded. The frequencies and intensities of vibronic bands, including the 0–0 band at 43,896 cm_-1, were measured An assignment of the frequencies of fundamental vibrations in the third electronically excited state is suggested The matrices of rotation and shift of normal coordinates due to electronic excitation are calculated, and the vibronic spectrum of pyridine N-oxide is interpreted on the basis of these matrices. Translated fromZhurnal Struktumoi Khimii, Vol. 38, No. 2, pp. 357–362, March–April, 1997.     

Theoretical investigation of doubly resonant IR-UV sum-frequency vibrational spectroscopy of binaphthol chiral solution

The doubly resonant IR-UV sum-frequency vibrational spectroscopy (SFVS) of 1,1'-bi-2-naphthol (BN) solution and its dispersion spectra are analyzed and computed using the ZINDO//AM1 calculation and the direct approach of Raman scattering tensor calculation, which is based on calculations of Franck-Condon factors and on differentiation of the electronic transition moments with respect to the vibrational normal modes. The calculated results indicate that, for the most intense vibrational bands observed in the SFVS experiment, the calculated frequencies, symmetry, order, intensities, and pattern of the enhanced vibrational modes agree with experiment qualitatively, and due to the Franck-Condon progression, there are the doublet peaks in the corresponding resonant sum-frequency dispersion spectra. The polarization resonance Raman spectra of BN for the vibrational modes appearing in SFVS are also computed and associated with the experiment SFVS of BN. This direct evaluation approach of Raman tensors may provide a way of assigning the doubly resonant IR-UV SFVS.     

Resonance Raman spectra of uracil based on Kramers-Kronig relations using time-dependent density functional calculations and multireference perturbation theory

The use of time-dependent density functional calculations for the optimization of excited-state structures and the subsequent calculation of resonance Raman intensities within the transform-theory framework is compared to calculations of Hartree-Fock/configuration interaction singles-type (CIS). The transform theory of resonance Raman scattering is based on Kramers-Kronig relations between polarizability tensor components and the optical absorption. Stationary points for the two lowest excited singlet states of uracil are optimized and characterized by means of numerical differentiation of analytical excited-state gradients. It is shown that the effect of electron correlation leads to substantial modifications of the relative intensities. Calculations of vibrational frequencies for ground and excited states are carried out, which show that the neglect of Duschinsky mixing and the assumption of equal wave numbers for ground and excited state are not in all cases good approximations. We also compare the transform-theory resonance Raman intensities with those obtained within a simple approximation from excited-state gradients at the ground-state equilibrium position, and find that they are in qualitative agreement in the case of CIS, but show some important differences in calculations based on density functional theory. Since the results from CIS calculations are in better agreement with experiment, we also present approximate resonance Raman spectra obtained using excited-state gradients from multireference perturbation theory calculations, which confirm the CIS gradients.     

Effect of scaling of a quantum mechanical force field on the frequencies and forms of molecular vibrations

The effect of scaling of an ab initio quantum mechanical force field on the frequencies and forms of normal vibrations are studied in terms of first- and second-order perturbation theory. Scaling the force constant matrix according to Pulay using certain assumptions in first-order perturbation theory is equivalent to scaling vibration frequencies and does not modify the form of vibrations. In this case, the second-order corrections to the frequencies and forms of vibrations become zero. The first-order perturbation theory formulas are used to verify the assumptions by calculating the frequencies and matrices of transition to perturbed forms of vibrations of ethane, propane, ethylene, cyclopropene, and isobutene molecules from quantum mechanical force fields found with the 6-31G basis set. It is shown that the vibration frequencies calculated by the formulas of first-order perturbation theory are in good agreement with exact values; the matrix of transition to perturbed eigenvectors is rarefied, with only ≈1% of its elements being markedly nonzero. Moscow State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 2, pp. 210–216, March–April, 1998. This work was supported by RFFR grant No. 96-03-34085.     

A chemometric analysis of ab initio vibrational frequencies and infrared intensities of methyl fluoride

Factorial design and principal component analyses are applied to CH₃F infrared frequencies and intensities calculated from ab initio wave functions. In the factorial analysis, the quantitative effects of changing from a 6–31G to a 6–311G basis, of including polarization and diffuse orbitals, and of correcting for electron correlation using the second-order Møller-Plesset procedure are determined for all frequencies and intensities. The most significant main effect observed for the frequencies corresponds to the shift from Hartree-Fock to MP2 calculations, which tends to lower all frequency values by approximately 100 cm⁻¹. For the intensities, the main effects are larger for the CF stretching and the CH₃ asymmetric stretching modes. Interaction effects between two or more of the four factors are found to be of minor importance, except for the interaction between correlation and polarization. The principal component analysis indicates that wave functions with polarization and diffuse orbitals at the second-order Møller-Plesset level provide the best estimates for the harmonic frequencies, but not for the intensities. For the frequencies, the first principal component distinguishes between MP2 and Hartree-Fock calculations, while the second component separates the wave functions with polarization orbitals from those without these orbitals. For the intensities, the separation is similar but less well defined. This analysis also shows that wave function optimization to calculate accurate intensities is more difficult than an optimization for frequencies. © 1996 by John Wiley & Sons, Inc.     

Vibrational spectra and stereochemistry of mono- and polysaccharides

A comparative study of the IR and Raman spectra of D-glucose anomers is reported. The spectra were found to differ between the anomers, despite the absence of symmetry elements in the anomer molecules. The results of theoretical calculations are systematized; it was found that the skeletal CiOi or CiO(i+1) (i=1, 2, 3, 4, 5) bond is characterized by a specific set of frequencies of normal vibrations, which have predominant contributions from the vibrations of atomic groups involving these bonds to the potential energy distribution (PED). The frequencies of normal vibrations with the major contribution to PED from CO and CC bonds are well separated and differ between the D-glucose anomers. The C5C6 bond has the greatest number of normal vibrations with predominant contributions to PED. Model calculations of vibrational spectra are reported for D-glucose anomers with modified (β→α and α→β) conformations of the CH₂OH group. B. I. Stepanov Institute of Physics, Belarus Academy of Sciences. Institute of Low Temperatures and Structural Studies, Polish Academy of Sciences, Wroclaw. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 2, pp. 322–329, March–April, 1995. Translated by L. Smolina     

Experimental and Density Functional Theory Calculation Studies on Raman and Infrared Spectra of 1,1'-Binaphthyl-2,2'-diamine

The IR absorption, visible excited normal Raman, and UV-excited near-resonant Raman (UVRR) spectra of 1,1'-binaphthyl-2,2'-diamine (BINAM) were measured and analyzed. Density functional theory calculations were carried out to investigate its vibrational frequencies, infrared absorption, normal Raman, and near-resonance Raman intensities. The observed Raman and IR bands of BINAM were assigned with respect to the local vibrations of substituted 2-naphthylamine. Several Raman bands of BINAM were found selectively enhanced in the UVRR in comparison with the normal Raman spectrum. Possible excited state geometry distortion was discussed based on the resonance Raman intensity analysis.     

Accurate theoretical IR and Raman spectrum of Al2O2 and Al2O3 molecules

The accurate harmonic vibration frequencies together with the infrared (IR) and Raman intensities of the most stable conformers of Al₂O₂ and Al₂O₃ molecules have been calculated by the density functional theory (DFT) method with B3LYP exchange–correlation potential and using a set of the augmented correlated consistent basis sets up to quintuple order. The anharmonic vibration frequencies of the non-linear Al₂O₂ molecule have also been calculated. The obtained equilibrium geometrical parameters, harmonic and anharmonic vibration frequencies along with the IR and Raman intensities good converge to their limits with increasing the size of the used basis set. A comparison of the calculated harmonic and anharmonic vibrational frequencies with the available experimental ones points out that the small differences between the calculated harmonic and experimental frequencies can be further substantially reduced when calculations of the anharmonic vibrational frequencies will be available for all types of molecular geometries.     

Density Functional Theoretical Analysis of the Molecular Structural Effects on Raman Spectra of β‐Carotene and Lycopene

The molecular structural and Raman spectroscopic characteristics of β‐carotene and lycopene are investigated by density functional calculations. The effects of molecular structure and solvent environment on the Raman spectra are analyzed by comparing the calculated and measured results. It is found that the B3LYP/6‐31G(d) method can predict the reasonable result for β‐carotene, but the ν1 Raman activities of lycopene overflow at all the used theoretical methods because of the longer conjugation length. The calculated results indicate that the rotation of β‐rings in β‐carotene impedes the delocalization of π‐electrons, shortens the effective conjugation length, and results in higher frequency and lower activity of the ν1 mode in β‐carotene than lycopene. The measured ν1 bands of β‐carotene and lycopene shift respectively to higher and lower frequencies in solution compared with that in crystals since the crystal packing forces can lead to different conformational variations in the carotenoids molecules. The polarized continuum model theoretical analysis suggests that solvent has slight (significant) effects on the Raman frequencies (intensities) of both carotenoids.     

Coupled calculation of vibrational frequencies and intensities

The combination of normal coordinate analysis with intensity calculations gives quantitative information about molecular force fields and the assignments of vibrational frequencies. Calculations of vibrational intensities by means of a standard CNDO/2 version give rise to satisfactory results for the IR intensities. However, the calculated Raman intensities often differ strongly from the experimental data. Inclusion of 2p-polarization functions on hydrogen in the usually used valence basis set is quite successful to obtain improved molecular polarizabilities as well as Raman intensities.     

Ab initio calculations of the ultraviolet resonance Raman spectra of uracil

An equation been derived to calculate, ab initio, the frequencies and intensities of a resonant Raman spectrum from the transform theory of resonance Raman scattering. This equation has been used to calculate the intensities of the ultraviolet resonance Raman spectra from the first π-π* excited state of uracil and 1,3-dideuterouracil. The protocol for this calculation is as follows: (1) The force constant matrix elements in Cartesian coordinate space, the vibrational frequencies, and the minimum energy ground and excited state geometries of the molecule are calculated ab initio using the molecular orbital program Gaussian 92, (2) the force constants in Cartesian coordinates are transformed into force constants in the space of a set of 3N – 6 nonredundant symmetrized internal coordinates, (3) the G matrix is constructed from the energy minimized ground state Cartesian coordinates and the GFL = LΛ eigenvalue equation is solved in internal coordinate space, (4) the elements of the L and L^?1 matrices are calculated, (5) the changes in all of the internal coordinates in going from the ground to the excited state are calculated, and (6) these results are used in combination with the transform theory of resonance Raman scattering to calculate the relative intensities of each of the 3N – 6 vibrations as a function of the exciting laser frequency. There are no adjustable parameters in this calculation, which reproduces the experimental frequencies and intensities with remarkable fidelity. This indicates that the Dushinsky rotation of the modes in the excited state of these molecules is not important and that the simplest form of the transform theory is adequate. © 1995 John Wiley & Sons, Inc.     

Estimation of the contribution of absorption bands for overtones and composite frequencies in IR spectra of olefins and heteroatomic organic compounds

Intensities of fundamental, overtone, and composite absorption bands for 11 olefins, 17 nitrogen- and oxygen-containing organic compounds, and 12 sulfur-containing organic compounds are calculated in the anharmonic approximation. The first and second derivatives of the electric dipole moment of a molecule were calculated by the quantum-chemical ab initio MP2/6-31G(1d) approach. It is shown that, for the studied compounds, the average contribution of overtones and composite frequencies to absorption in the region from 100 to 4000 cm⁻¹ is of about 10%. The major contribution (on the average 80%) of overtones and composite frequencies falls in the regions (mainly from 1600 to 2800 cm⁻¹) where fundamental transitions are rarely observed. The calculations well describe the centers and intensities of the fundamental, overtone, and composite absorption bands and can be used for the standard-free spectrochemical determination of the compounds of interest by their overtone spectra.     

In situ resonant Raman and ESR spectroelectrochemical study of electrochemically synthesized poly(<Emphasis Type="Italic">p</Emphasis>-phenylenevinylene)

The electrochemical synthesis of poly(p-phenylenevinylene) (PPV) and different modifications in the electronic distribution upon electrochemical p-doping (oxidation) and n-doping (reduction) of this polymer film have been studied in situ by resonance Raman spectroscopy, optical absorption spectroscopy and ESR spectroscopy. The polymer film has been prepared by electrochemical reduction of α,α,α′,α′-tetrabromo-p-xylene in dimethylformamide using tetraethylammonium tetrafluoroborate as the electrolyte salt. During electrochemical polymerization the position and relative intensities of the Raman bands change regularly as the chain length increases and finally converge on values reported for chemically prepared PPV. The Raman spectra for electrochemically polymerized PPV is compared to infrared-active vibration bands for electrochemically n-doped PPV. When the polymer undergoes redox reactions (doping-dedoping), shifts and broadening of Raman bands, compared to neutral PPV, are observed. Interpretation of the Raman spectra and the ESR results led to the conclusion that charge transfer in this system is mainly accomplished by polaron species formed upon doping of the polymer. In this reaction the quinoid structure is formed rather than the benzenoid structure. Electronic Publication     

Effect of structural characteristics of water on the infrared absorption and raman spectra

An analysis of band contour in the IR absorption (overtone region) and Raman spectra of water suggests that the high-frequency components of spectral bands correspond to a single continuous distribution in energy of H-bonds. A local increase in the probability density function at high frequencies, which leads to an increase in the population of states with weak hydrogen bonds, is caused by the specific behavior of the angular dependence of the energy of hydrogen bonds between water molecules. St. Petersburg State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 3, pp. 467–472, May–June, 1995. Translated by I. Izvekova     

Vibrational spectra and noncovalent interactions of carbohydrates molecules

The differences between the vibrational spectra of carbohydrates of the same chemical structure caused by the noncovalent intra- and intermolecular interactions have been systematized. In the general case, these differences show up as the following specific features of changes in the bond intensities: change in the intensity ratio of closely spaced bands (IR and Raman spectra); selective change (increase, decrease) in intensities of individual bands (IR and Raman spectra); change (increase, decrease) in intensities of practically all bands (IR and Raman spectra); appearance of strong bands in the region of low frequencies from 50 to 200 cm⁻¹ (Raman spectra); appearance of strong diffuse bands in the low-frequency range with a simultaneous great reduction in the other bands (practical disappearance of the majority of bands) (Raman Spectra). The causes of such a kind of changes in the band intensities in the vibrational spectra of carbohydrates are discussed.     

Characteristics of the Raman spectra of single-walled carbon nanotube bundles under electrochemical potential control

Resonant Raman scattering spectra of single-walled carbon nanotube–sodium dodecyl sulfate (SWNT–SDS) bundles adsorbed on Au electrodes have been investigated in aqueous electrolytes. Raman intensities of the radial breathing mode (RBM) with 785-nm laser excitation were monitored at different electrode potentials between −0.5 and +0.8 V relative to the SCE. Six resolved RBM peaks assignable to different diameter tubes all decreased in intensity when the electrode was positively biased, because of depletion of valence-band electrons associated with resonant excitation. The attenuation occurred at more positive potentials for narrower-diameter tubes with higher RBM frequencies consistent with their larger bandgaps. The results suggest the Fermi level is equilibrated in bundled SWNTs in contrast with the large Fermi-level shifts reported for isolated SWNTs.     

Infrared and Raman Spectroscopy of Methylcyanodiacetylene (CH3C5N)

A spectroscopic study combining IR absorption and Raman scattering is presented for methylcyanodiacetylene (CH₃C₅N). Gas‐phase, cryogenic matrix‐isolated, and pure solid‐phase substance was analyzed. Out of 16 normal vibrational modes, 14 were directly observed. The analysis of the spectra was assisted by quantum chemical calculations of vibrational frequencies, IR absorption intensities, and Raman scattering activities at density functional theory and ab initio levels. Previous assignments of gas‐phase IR absorption bands were revisited and extended.